ObservabilityTest: A maple package that test observability/identifiability of ordinary differential systems in polynomial time. Bibliographic reference (citing this package): A probabilistic algorithm to test local algebraic observability in polynomial time. The following questions are often encountered in system and control theory. Given an algebraic model of a physical process, which variables can be, in theory, deduced from the input-output behavior of an experiment? How many of the remaining variables should we assume to be known in order to determine all the others? These questions are parts of the local algebraic observability problem which is concerned with the existence of a non trivial Lie subalgebra of the symmetries of the model letting the inputs and the outputs invariant. We present a probabilistic seminumerical algorithm that proposes a solution to this problem in polynomial time. A bound for the necessary number of arithmetic operations on the rational field is presented. This bound is polynomial in the complexity of evaluation of the model and in the number of variables. Furthermore, we show that the size of the integers involved in the computations is polynomial in the number of variables and in the degree of the system. Last, we estimate the probability of success of our algorithm.

References in zbMATH (referenced in 20 articles , 1 standard article )

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  1. Boulier, François; Lemaire, François; Rosenkranz, Markus; Ushirobira, Rosane; Verdière, Nathalie: On symbolic approaches to integro-differential equations (2020)
  2. Mozharovskiĭ, I. S.; Samotylova, S. A.; Torgashov, A. Yu.: Predictive modeling of mass-transfer technological plant using an algorithm of alternating conditional expectations (2020)
  3. Farkhatdinov, Ildar; Michalska, Hannah; Berthoz, Alain; Hayward, Vincent: Gravito-inertial ambiguity resolved through head stabilization (2019)
  4. Jeronimo, Gabriela; Pérez Millán, Mercedes; Solernó, Pablo: Identifiability from a few species for a class of biochemical reaction networks (2019)
  5. Villaverde, Alejandro F.: Observability and structural identifiability of nonlinear biological systems (2019)
  6. Lang, Moritz; Stelling, Jörg: Modular parameter identification of biomolecular networks (2016)
  7. Letham, Benjamin; Letham, Portia A.; Rudin, Cynthia; Browne, Edward P.: Prediction uncertainty and optimal experimental design for learning dynamical systems (2016)
  8. Stigter, Johannes D.; Molenaar, Jaap: A fast algorithm to assess local structural identifiability (2015)
  9. Wongvanich, N.; Hann, C. E.; Sirisena, H. R.: Robust global identifiability theory using potentials -- application to compartmental models (2015)
  10. Anguelova, Milena; Karlsson, Johan; Jirstrand, Mats: Minimal output sets for identifiability (2012)
  11. Anguelova, Milena; Wennberg, Bernt: On analytic and algebraic observability of nonlinear delay systems (2010)
  12. Wu, Wenyuan; Reid, Greg; Ilie, Silvana: Implicit Riquier bases for PDAE and their semi-discretizations (2009)
  13. Yates, James W. T.; Evans, Neil D.; Chappell, Michael J.: Structural identifiability analysis via symmetries of differential equations (2009)
  14. Anguelova, Milena; Wennberg, Bernt: State elimination and identifiability of the delay parameter for nonlinear time-delay systems (2008)
  15. Jiménez-Hornero, Jorge E.; Santos-Dueñas, Inés M.; García-García, Isidoro: Structural identifiability of a model for the acetic acid fermentation process (2008)
  16. D’Alfonso, Lisi; Jeronimo, Gabriela; Solernó, Pablo: On the complexity of the resolvent representation of some prime differential ideals (2006)
  17. Margaria, Gabriella; Riccomagno, Eva; White, Lisa J.: Structural identifiability analysis of some highly structured families of statespace models using differential algebra (2004)
  18. Matera, G.; Sedoglavic, A.: Fast computation of discrete invariants associated to a differential rational mapping (2003)
  19. Sedoglavic, Alexandre: A probabilistic algorithm to test local algebraic observability in polynomial time (2002)
  20. Sedoglavic, Alexandre: A probabilistic algorithm to test local algebraic observability in polynomial time (2001)